Preliminaries: Peel eggplant and cut into 1/4-inch slices; brush both sides of each eggplant slice with olive oil. Slice red peppers from top to bottom; remove stems, cores and seeds. Peel and slice onion, remove stems from mushrooms. Brush both sides of red onion slices and portobello with oil.

Grill the vegetables: Grill eggplant slices until they are golden brown, the bell peppers until they are charred, the onion until it is soft, and the portobello until it is tender and cooked through. Immediately place roasted red peppers in a paper bag and close the top. Allow peppers to stand several minutes, then peel.

Assemble the sandwiches: Lay tortillas or flatbreads on work surface. Cut eggplant slices in half, and place four halves over the left third of each wrap. Cut peppers into 1/2-inch-wide strips, and lay about half of a pepper atop the eggplant on each wrap. Top peppers with a couple of onion slices. Cut each portobello into slices, and divide among sandwiches, over onion slices. Sprinkle about 1/4 cup feta cheese over vegetables. Fold over flatbreads and tightly roll each into a fat log.